$1000 invested at an APR of 9% for 9 years. If interest is compounded annually, what is the amount of money after nine years?
To calculate the amount of money after nine years when $1000 is invested at an Annual Percentage Rate (APR) of 9% and the interest is compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Let's substitute the given values into the formula:
P = $1000
r = 9% = 0.09 (converted to decimal)
n = 1 (compounded annually)
t = 9 years
A = 1000(1 + 0.09/1)^(1*9)
Simplifying the formula:
A = 1000(1.09)^9
Now, we can calculate the amount after nine years using this formula.
P = Po(1+r)^n.
r = 0.09 = APR expressed as a decimal.
n = 1Comp./yr * 9yes = 9 Compounding periods.
Plug the above values into the given Eq
and solve for P.
Answer: P = $2171.89